Separating temporal and topological effects in walk-based network centrality

TL;DR

This paper analyzes how temporal and structural factors influence walk-based network centrality metrics, providing formulas to predict their expectations and methods to distinguish these effects in real data.

Contribution

It introduces analytical formulas to separate temporal and structural influences on dynamic communicability scores in temporal networks.

Findings

Formulas accurately predict expected broadcast and receive scores after shuffling.

Temporal variation can be controlled when computing dynamic centrality.

Scores can often be approximated by row and column sums of a matrix exponential.

Abstract

The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node with respect to a model of contagion based on time-respecting walks. This article examines the temporal and structural factors influencing these metrics by considering a versatile stochastic temporal network model. We analytically derive formulae to accurately predict the expectation of the broadcast and receive scores when one or more columns in a temporal edge-list are shuffled. These methods are then applied to two publicly available data-sets and we quantify how much the centrality of each individual depends on structural or temporal influences. From our analysis we highlight two practical contributions: a way to control for temporal variation when computing dynamic communicability, and the conclusion that the broadcast and receive scores can, under a range of circumstances, be replaced by the row and column sums of the matrix exponential of a weighted adjacency matrix given by the data.